Flip Operator

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which, by modulo
indexing, is . The operator reverses the order of samples through
of a
sequence, leaving sample alone, as shown in Fig. 8.1a.
Thanks to modulo indexing, it can also be viewed as “flipping” the
sequence about the vertical axis, as shown in Fig. 8.1b.
The interpretation of Fig. 8.1b
is usually the one we want, and the operator is usually thought of as “time reversal” when
applied to a signal or “frequency
reversal” when applied to a spectrum .

Figure 8.1:Illustration of
and
for
and two different domain interpretations: a) . b)
.